SOLUTION: A woman standing on a hill sees a flagpole that she knows is 60 ft tall. The angle of depression to the bottom of the pole is 14�, and the angle of elevation to the top of the pol

Question 661252: A woman standing on a hill sees a flagpole that she knows is 60 ft tall. The angle of depression to the bottom of the pole is 14�, and the angle of elevation to the top of the pole is 18�. Find her distance x from the pole. (Round your answer to one decimal place.)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A woman standing on a hill sees a flagpole that she knows is 60 ft tall. The angle of depression to the bottom of the pole is 14�, and the angle of elevation to the top of the pole is 18�. Find her distance x from the pole. (Round your answer to one decimal place.)
**
draw the following diagram:
from the top of the hill draw a line 18� above horizontal to the top of the 60 ft pole
from the top of the hill draw a line 14� below horizontal to the bottom of the 60 ft pole
you now have 2 right triangles sharing a common horizontal line=x to the pole
let d=part of pole above horizontal line
60-d=part of pole below horizontal line
2 equations:
d/x=tan 18�
60-d/x=tan 14�
..
x=d/tan 18�
x=(60-d)/tan 14�
..
d/tan 18�=(60-d)/tan 14�
tan 14�d=tan 18�(60-d)
tan 14�d=tan 18�*60-tan 18�d
tan 14�d+tan 18�d=tan 18�*60
d(tan 14�+tan 18�)=tan 18�*60
d=tan 18�*60/(tan 14�+tan 18�)
x=d/tan 18�=60/(tan 14�+tan 18�)=104.5 ft
her distance x from the pole=104.5 ft

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